Space is not going to save us any time soon, people suck at restraining themself and given our current situation we can approximate our planet to a close system with finite resources.
So yeah, I'd go with less babies. Or more deaths, but one is more pleasant.
If the whole world reaches Mumbai's density (75k/sq mile), we would host 15 trillion people. Now, no matter what projections you hear from anyone, you never hear a peak population of more than 50 billion, so you are off by a factor of 300.
Here's for example the latest UN prediction up to 2100. You'll notice a 95% estimate that we'll be below 13 billion.
[1] https://population.un.org/wpp/Graphs/Probabilistic/POP/TOT/9...
What's more, the vast majority of indian population consumme much less than the average american.
Democracy, health care, education, respect of the individual, peace... All that are affected, at various degree of overpopulation. There is not need to mirror your stats.